Graph Contrastive Learning for Clustering of Multi-Layer Networks

Multi-layer networks precisely model complex systems in society and nature with various types of interactions, and identifying conserved modules that are well-connected in all layers is of great significance for revealing their structure-function relationships. Current algorithms are criticized for either ignoring the intrinsic relations among various layers, or failing to learn discriminative features. To attack these limitations, a novel graph contrastive learning framework for clustering of multi-layer networks is proposed by joining nonnegative matrix factorization and graph contrastive learning (called jNMF-GCL), where the intrinsic structure and discriminative of features are simultaneously addressed. Specifically, features of vertices are firstly learned by preserving the conserved structure in multi-layer networks with matrix factorization, and then jNMF-GCL learns an affinity structure of vertices by manipulating features of various layers. To enhance quality of features, contrastive learning is executed by selecting the positive and negative samples from the constructed affinity graph, which significantly improves discriminative of features. Finally, jNMF-GCL incorporates feature learning, construction of affinity graph, contrastive learning and clustering into an overall objective, where global and local structural information are seamlessly fused, providing a more effective way to describe structure of multi-layer networks. Extensive experiments conducted on both artificial and real-world networks have shown the superior performance of jNMF-GCL over state-of-the-art models across various metrics.